Question

假设 $10$ 根香蕉中的 $\dfrac{2}{3}$ 与 $8$ 个橙子价值相同。那么 $5$ 根香蕉中的 $\dfrac{1}{2}$ 与多少个橙子价值相同？

Suppose that $\dfrac{2}{3}$ of $10$ bananas are worth as much as $8$ oranges. How many oranges are worth as much as $\dfrac{1}{2}$ of $5$ bananas?

$2$

$\dfrac{5}{2}$

$3$

$\dfrac{7}{2}$

$4$

因为 $10$ 根香蕉的 $\dfrac{2}{3}$ 是 $\dfrac{20}{3}$ 根香蕉，价值等于 $8$ 个橙子，所以一根香蕉相当于 $8 \div \dfrac{20}{3} = \dfrac{6}{5}$ 个橙子。

$5$ 根香蕉的 $\dfrac{1}{2}$ 是 $\dfrac{5}{2}$ 根香蕉，价值为 $\dfrac{5}{2} \cdot \dfrac{6}{5} = 3$ 个橙子。

所以正确答案是 C。

Since $\dfrac{2}{3}$ of $10$ bananas is $\dfrac{20}{3}$ bananas worth $8$ oranges, one banana is worth $8 \div \dfrac{20}{3} = \dfrac{6}{5}$ oranges.

Now $\dfrac{1}{2}$ of $5$ bananas is $\dfrac{5}{2}$ bananas, worth $\dfrac{5}{2} \cdot \dfrac{6}{5} = 3$ oranges.

Thus, the correct answer is C.